If f:(0,∞)→(0,∞) satisfy f(xf(y))=x3ya(a∈R),then ∑r=1nf(r) Cr n is equal to

x=1⇒f(f(y))=ya,f(y)=1x⇒f(1)=ya(f(y))3,y=1⇒(f(1))4=1, f(x)=x3

If f:(0,∞)→(0,∞) satisfy f(xf(y))=x3ya(a∈R),then ∑r=1nf(r) Cr n is equal to

x=1⇒f(f(y))=ya,f(y)=1x⇒f(1)=ya(f(y))3,y=1⇒(f(1))4=1, f(x)=x3

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If $f : (0, \infty) \to (0, \infty)$ satisfy $f (x f (y)) = x^{3} y^{a} (a \in R), t h e n \sum_{r = 1}^{n} f (r) {}^{n}C_{r}$ is equal to

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$n (n - 3) 2^{n + 3}$

$n^{2} (n - 3) 2^{n + 3}$

$n (n + 3) 2^{n - 3}$

$n^{2} (n + 3) 2^{n - 3}$

answer is C.

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$x = 1 \Rightarrow f (f (y)) = y^{a}, f (y) = \frac{1}{x} \Rightarrow f (1) = \frac{y^{a}}{{(f (y))}^{3}}, y = 1 \Rightarrow {(f (1))}^{4} = 1, f (x) = x^{3}$

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If f:(0,∞)→(0,∞) satisfy f(xf(y))=x3ya(a∈R),then ∑r=1nf(r) Cr n is equal to

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If $f : (0, \infty) \to (0, \infty)$ satisfy $f (x f (y)) = x^{3} y^{a} (a \in R), t h e n \sum_{r = 1}^{n} f (r) {}^{n}C_{r}$ is equal to